JACKSON HOLE, Wyo. — Conservative activists who want the Federal Reserve to raise interest rates distributed chocolate coins in golden wrappers at the local airport last week as Fed officials arrived for their annual policy retreat.

Liberal activists in green “Whose Recovery?” T-shirts formed a receiving line at the resort hotel in the heart of Grand Teton National Park where the meeting was held, to personalize their argument that the Fed should wait.

Sometime soon — possibly as early as mid-September and probably no later than the end of the year — the Fed plans to raise its benchmark interest rate one-quarter of one percentage point, a mathematically minor move that has become a very big deal.

Investors, who always pay attention to the Fed, are paying particular attention now. The central bank has held short-term rates near zero since December 2008; the impending end of that era is one cause of recent financial market turmoil.

But the Fed’s plans have also become the latest point of contention in a broader debate about the government’s management of the American economy, pitting liberals who see a need for more aggressive measures to bolster growth against conservatives concerned that Washington and the Fed are already doing much too much.

“There shouldn’t be this intense interest in a quarter-point increase, and there shouldn’t be this intense interest in whether it comes in September or December,” said Alan S. Blinder, a Princeton economist and the Fed’s vice chairman in the mid-1990s. “But the Fed remains the center of the financial universe. People stare at it like they stare at the North Star.”

And so, as Fed officials conferred with other central bankers and academics, the liberal activists held two days of “Fed Up” teach-ins in a room directly below the main conference, while the conservatives convened a “Jackson Hole Summit” at a nearby dude ranch.

In the decades before the financial crisis, policy makers generally agreed that central banks should focus on moderating inflation. Now, both that goal and the best way to achieve it are subjects of debate. Liberals argue that the Fed should aim more broadly to lower unemployment and encourage rising living standards. Conservatives want to strengthen the focus on inflation by requiring officials to follow rules in making policy.

With the critics lining up outside, central bankers found no escape inside the main conference, where a series of academics warned policy makers that their view of inflation was oversimplified, and that their policies were less effective as a consequence.

“The conference was more about what we don’t know, about a candid willingness to analyze what we don’t know,” said Lucrezia Reichlin, a professor at London Business School and former director general of research at the European Central Bank. “It did not really inspire confidence” in monetary policy.

The formal program, on “Inflation Dynamics and Monetary Policy,” was devoted to the vexing reality that inflation in recent years has not behaved as economists predicted. The basic paradigm, known as the Phillips Curve, is that inflation falls as unemployment rises, and rises as unemployment falls. But inflation did not fall as much as expected during the Great Recession, and it has remained surprisingly weak during the recovery.

Over the course of two days, the invited academics argued that the real story was more complicated. One study, for example, presented evidence that prices fall more slowly during recessions because cash-short firms actually tend to increase prices in the face of declining demand for their products.

“Once you integrate all these dynamics, it may turn out that life is not that simple,” said Eric M. Leeper, an economist at Indiana University and co-author of a paper arguing that central banks need better economic models.

Central bankers, however, have shown little interest in paradigm shifts. Several said that the basic understanding of inflation, while obviously imperfect, remains more functional than any alternatives.

“I don’t think the folks at the Fed are of a mind to redesign monetary policy just because of what happened during the crisis,” said Jon Faust, a professor of economics at Johns Hopkins University and a former adviser to the Fed’s chairwoman, Janet L. Yellen, and her predecessor, Ben S. Bernanke.

Indeed, Vítor Constâncio, vice president of the European Central Bank, said the euro area was currently experiencing “a renaissance of the Phillips Curve.”

But his bottom line, too, was that the Fed understands inflation well enough to predict its movements. While domestic inflation has been surprisingly sluggish for years now, Mr. Fischer said on Friday that his confidence in an eventual rebound remained “pretty high.”

The organizers of the fringe conferences acknowledged the odds against their more radical proposals.

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When it comes to raising or lowering interest rates, what the Fed is really trying to do is balance growth and inflation. But they have a limited set of tools to accomplish their goal.Published OnJuly 29, 2015CreditImage by Aaron Byrd/The New York Times

Jim DeMint, president of the Heritage Foundation, spoke at the conservative conference of “a long and difficult battle that we can and must win.”

The Center for Popular Democracy, which organized the “Fed Up” campaign, wants the Fed to keep rates near zero even as overall unemployment falls, to spur wage gains and help members of minorities, in particular, find jobs. It brought about 50 people to Jackson Hole as part of an effort to engage community groups that generally focus on civil rights or local issues like minimum wage laws.

Dawn O’Neal, 48, makes $8.50 an hour as a day care worker in suburban Atlanta; her husband has not found regular construction work in a year. When Ms. O’Neal needs a refill on her asthma medication, she cuts back on food, buying hot dogs instead of beef and canned vegetables instead of fresh vegetables.

“I don’t feel like anyone at the Fed has ever had to make a decision about whether to eat or get medication, and so when I hear that they’re going to raise interest rates in September, it angers me and it scares me,” Ms. O’Neal said.

The protesters struck a chord with some officials at the main meeting. Jason Furman, President Obama’s chief economic adviser, went downstairs and delivered an impromptu speech. “We don’t comment on monetary policy, but what I can say is that monetary policy matters,” he told the activists. The prosperity of the late 1990s, he added, resulted in part from “a set of decisions made by the Federal Reserve that allowed that to happen.”

Other officials, however, said the push for low rates was misguided.

“The biggest risk for those that are less fortunate is that we would go back into recession,” said James Bullard, president of the Federal Reserve Bank of St. Louis, who said he leaned toward raising rates in September. “I’m hoping my policy would lengthen out the expansion longer.”

This view has few fans among the central bankers, who see their own judgment as an essential part of policy making.

Mr. Blinder said part of the disconnect between the officials and the activists may reflect that broader concerns motivate liberals and conservatives. Conservatives see the Fed as enabling the growth of the federal debt, while liberals see the Fed as contributing to the rise of inequality.

Mr. Blinder said the central bank had little power to reverse either trend. “They overstate the importance and power of the Federal Reserve,” he said. All it can do, he added, is “address these problems around the edges.”

Correction:

An article on Monday about pressure on the Federal Reserve from groups with differing ideas on when the Fed should raise interest rates misidentified, in some editions, the group that organized the “Fed Up” campaign, which wants the Fed to keep rates low, to lower unemployment rates and to raise living standards. It is the Center for Popular Democracy, not the Center for Public Democracy.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Left and Right Work to Shift Fed’s Direction. Order Reprints | Today’s Paper | Subscribe